Weber–Fechner law and Regional Bell Operating Company: Difference between pages

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{{redirect|Baby Bell|Babybel cheese|Babybel}}
The '''Weber–Fechner law''' attempts to describe the relationship between the physical magnitudes of [[Stimulus (physiology)|stimuli]] and the perceived intensity of the stimuli. [[Ernst Heinrich Weber]] (1795–1878) was one of the first people to approach the study of the human response to a [[physical stimulus]] in a [[quantitative]] fashion. [[Gustav Fechner|Gustav Theodor Fechner]] (1801–1887) later offered an elaborate theoretical interpretation of Weber's findings, which he called simply '''Weber's law''', though his admirers{{who}} made the law's name a hyphenate.{{fact|date=July 2008}}
{{Refimprove|date=October 2008}}


[[Image:RBOC map.png|thumb|400px|right|Map of the original and current companies.]]
== Background ==
The '''Regional Bell Operating Companies''' ('''RBOC''') are the result of the U.S. Department of Justice [[antitrust]] suit against the former [[American Telephone & Telegraph]] Company (later known as AT&T Corp.)
[[Stevens' power law]] is sometimes{{when}} considered more accurate and general, although both make assumptions about the measurement of perceived intensity. The Weber–Fechner law assumes that [[just noticeable difference]]s are additive. [[L. L. Thurstone]] uses this assumption for the concept of discriminal dispersion in the [[Law of comparative judgment]].


==History==
Fechner believed that Weber had discovered the fundamental principle of mind-body interaction, a mathematical analog of the function [[René Descartes]] once assigned to the [[pineal gland]].
On [[January 8]], [[1982]], AT&T Corp. settled the suit and agreed to divest ("spin off") its local exchange service operating companies. Effective [[January 1]], [[1984]], AT&T Corp.'s local operations were split into seven independent Regional Bell Operating Companies known as "Baby Bells." RBOCs were originally known as '''Regional Holding Companies''', or '''RHCs''' <sup>[1]</sup>.


After the [[Modification of Final Judgment]], the resulting ''Baby Bells'' were originally:
== The case of weight ==
In one of his experiments, Weber gradually increased the weight that a blindfolded man was holding and asked him to respond when he first felt the increase. Weber found that the smallest noticeable difference in weight (the least difference that the test person can still perceive as a difference), was proportional to the starting value of the weight. That is to say, if the weight is 1 kg, an increase of a few grams will not be noticed. Rather, when the mass is increased by a certain factor, an increase in weight is perceived. If the mass is doubled, the threshold called smallest noticeable difference also doubles. This kind of relationship can be described by a differential equation as,


* [[Ameritech]] — (acquired by [[SBC Communications|SBC]] in 1999)
:<math> dp = k\frac{dS}{S} , \,\!</math>
* [[Bell Atlantic]] — (acquired [[GTE]] in 2000 and changed its name to [[Verizon]])
* [[BellSouth]] — (acquired by [[AT&T]] Inc. in 2006)
* [[NYNEX]] — (acquired by Bell Atlantic in 1996)
* [[Pacific Telesis]] — (acquired by SBC in 1997)
* [[Southwestern Bell Corporation|Southwestern Bell]] — (changed its name to SBC in 1995; acquired [[American Telephone & Telegraph Company|AT&T Corp.]] in 2005 and changed its name to [[AT&T]] Inc.)
* [[U S West]] — (acquired by [[Qwest]] in 2000)


Prior to 1984, AT&T Corp. also held investments in two smaller and otherwise independent companies, [[Cincinnati Bell]] and [[Southern New England Telephone]] (SNET). Following the 1984 breakup, these became fully independent as well. All nine local-exchange companies were assigned a share of the rights to the Bell trademark. Additionally, there was one comparably-sized independent (non-Bell) company, [[GTE]].
where ''dp'' is the differential change in perception, ''dS'' is the differential increase in the stimulus and ''S'' is the stimulus at the instant. A constant factor ''k'' is to be determined experimentally.


===Shared trademarks===
Integrating the above equation gives
After divestiture AT&T Corp. was prohibited from using the Bell name or logo (with the notable exception of AT&T's [[Bell Laboratories]]), and those trademarks would be shared by the RBOCs. Since the BellSouth acquisition, Cincinnati Bell has been the only former AT&T company still carrying the "Bell" name. (Additionally, [[Bell Canada]], which was separated from AT&T in 1956, continues to use the "Bell" trademark, which it owns outright in Canada.)


[[Verizon]] continues to use the Bell logo on its payphones (including former [[GTE]] payphones), hard hats, trucks, and buildings. As well, [[Malheur Bell]], an autonomous local phone company owned by [[Qwest Corporation|Qwest]], uses the Bell name and logo. In both cases, these are likely intended to display continued use in order to maintain the companies' respective trademark rights.
:<math> p = k \ln{S} + C, \,\!</math>


On the other hand, excluding historical documents and residual usage on the former BellSouth website, AT&T Inc. does not presently make any active use of the Bell marks.
where <math>C</math> is the [[constant of integration]], ln is the [[natural logarithm]].


===Original 1984 Regional Holding Company logos===
To determine <math>C</math>, put <math>p = 0</math>, i.e. no perception; then
<gallery>
Image:Nynex.svg|[[NYNEX]]
Image:Bell Atlantic logo (1984).svg|[[Verizon|Bell Atlantic]]
Image:BellSouth 1984 logo.svg|[[BellSouth]]
Image:Ameritech 1984 logo.svg|[[Ameritech]]
Image:Southwestern Bell logo (1984).svg|[[AT&T|Southwestern Bell]]
Image:US West logo.svg|[[US West]]
Image:Pacific Telesis logo.svg|[[Pacific Telesis]]
Image:AT&T logo (1984).svg|[[American Telephone & Telegraph|AT&T]]<br>(shown for comparison)
</gallery>


==Mergers==
:<math> C = -k\ln{S_0}, \,\!</math>
<!-- [[Image:RBOCs_Dec_06.jpg|thumb|320px|This diagram shows how the various RBOC companies have changed due to mergers and acquisitions since the 1984 breakup.]] -->
Many of these companies have since merged, leaving only 3 regional telephone companies in the United States. After the 1984 breakup, part of AT&T Corp.'s [[Bell Labs]] was split off into [[Bellcore]], which would serve as an R&D and standards body for the seven Baby Bells. In 1997, [[Bellcore]] was acquired by [[Science Applications International Corporation]] where it became a wholly owned subsidiary and was renamed [[Telcordia]].<ref>Dr. J. Robert Beyster with Peter Economy, The SAIC Solution: How We Built an $8 Billion Employee-Owned Technology Company, John Wiley & Sons (2007) p.73</ref>


=== AT&T Inc. ===
where <math>S_0</math> is that threshold of stimulus below which it is not perceived at all.
[[AT&T|Southwestern Bell Corporation]], which changed its name to [[SBC Communications]] in 1995, acquired [[Pacific Telesis]] in 1997, former independent Bell System franchise not part of divestiture, [[SNET]] in 1998, and [[Ameritech]] in 1999. In February 2005, SBC announced its plans to acquire former parent company [[Old AT&T|AT&T Corp.]] for over $16 billion. SBC took on the AT&T name upon merger closure on [[November 18]], [[2005]]. SBC began trading as [[AT&T|AT&T Inc.]] on [[December 1]], [[2005]] but began re-branding as early as November 21. On [[March 5]], [[2006]], it was announced that [[AT&T]] Inc. [http://biz.yahoo.com/ap/060305/at_t_bellsouth.html?.v=16 would purchase] [[BellSouth]] for $67 billion U.S., in an all-stock deal. On [[December 29]], [[2006]], the [[FCC]] approved the merger, worth $86 billion US. [http://money.cnn.com/2006/12/29/news/companies/att_bellsouth/?postversion=2006122919]


=== Verizon Communications ===
Therefore, our equation becomes
In 1997, [[NYNEX]] was acquired by [[Bell Atlantic]] (taking the [[Bell Atlantic]] name), which later, in 2000, merged with [[GTE]], the largest independent telephone company, to form [[Verizon]]. In 2005, following a protracted bidding war with rival RBOC Qwest, Verizon announced that it would acquire long distance company [[MCI Inc.|MCI]]. The Verizon and MCI merger closed on [[January 6]], [[2006]].


On [[January 16]], [[2007]], Verizon announced that it would split off [[Verizon New England]] operations in [[Maine]], [[New Hampshire]], and [[Vermont]] into a separate operating company, which then will be spun off and merged with [[FairPoint Communications]]. The deal was completed on March 31, 2008.
:<math> p = k \ln{\frac{S}{S_0}}. \,\!</math>


=== Qwest ===
The relationship between stimulus and perception is [[logarithmic scale|logarithmic]]. This logarithmic relationship means that if a stimulus varies as a [[geometric progression]] (i.e. multiplied by a fixed factor), the corresponding perception is altered in an [[arithmetic progression]] (i.e. in additive constant amounts). For example, if a stimulus is tripled in strength (i.e, 3 x 1), the corresponding perception may be two times as strong as its original value (i.e., 1 + 1). If the stimulus is again tripled in strength (i.e., 3 x 3 x 1), the corresponding perception will be three times as strong as its original value (i.e., 1 + 1 + 1). Hence, for multiplications in stimulus strength, the strength of perception only adds.
In 2000, [[US West]] was merged into [[Qwest]], a [[Denver]]-based [[fiber optics]] long-distance company. Also provides internet, wireless, and local telephone services.<ref>{{cite web |url=http://www.qwest.com |title=Qwest Homepage |accessdate=2008-01-20 |publisher=Qwest Communications International Inc. }}</ref>
=== Cincinnati Bell ===
* The former independent [[Bell System]] franchise [[Cincinnati Bell]], which was not part of the 1984 divestiture because AT&T only held a minority stake in the company, remains independent of the RBOCs.
=== Bell Canada ===
*[[Bell Canada]] was divested from AT&T Corp. in 1956 and not part of the 1984 agreement.


==Notes==
This logarithmic relationship is valid, not just for the sensation of weight, but for other stimuli and our sensory perceptions as well.
# The acronym '''RHC''' for '''Regional Holding Company''' is also sometimes seen.


==See also==
In addition, the mathematical derivations of the torques on a simple beam balance produce a description that is strictly compatible with Weber's law (see [http://cogprints.org/4094/ link1] or [http://www.bio-balance.com/Ref.htm link2]).
*[[Incumbent local exchange carrier]] (ILEC)
*[[Competitive local exchange carrier]] (CLEC)
*[[Telcordia Technologies|Bellcore]] (now known as [[Telcordia Technologies|Telcordia]])
*[[Local access and transport area]] (LATA)
*[[Bell System Divestiture]]


== The case of vision ==
== References ==
{{reflist}}
The eye senses [[brightness]] logarithmically. Hence [[stellar magnitude]] is measured on a logarithmic scale. This magnitude scale was invented by the ancient Greek astronomer [[Hipparchus]] in about 150 B.C. He ranked the stars he could see in terms of their brightness, with 1 representing the brightest down to 6 representing the faintest, though now the scale has been extended beyond these limits. An increase in 5 magnitudes corresponds to a decrease in brightness by a factor of 100.


==External links==
== The case of sound ==
* [http://www.bellsystemmemorial.com/images/bocmap.gif Pre-divestiture RBOC map (from Bell System Memorial)'''(dead link)''']
Still another logarithmic scale is the [[decibel]] scale of [[sound]] intensity. And yet another is [[Pitch (music)|pitch]], which, however, differs from the other cases in that the physical quantity involved is not a "strength".
* [http://www.bellsystemmemorial.com/table_of_changes.html Table of RBOC changes (from Bell System Memorial)'''(dead link)''']

* [http://www.qwest.com/ Qwest Communications]
In the case of perception of pitch, humans hear pitch in a logarithmic or [[Geometric progression|geometric]] ratio-based fashion: For notes spaced equally apart to the human ear, the [[Frequency|frequencies]] are related by a multiplicative factor. For instance, the frequency of corresponding notes of adjacent octaves differ by a factor of 2. Similarly, the perceived difference in pitch between 100 Hz and 150 Hz is the same as between 1000 Hz and 1500 Hz. Musical scales are always based on geometric relationships for this reason. Notation and theory about music often refers to pitch intervals in an additive way, which makes sense if one considers the logarithms of the frequencies, as <math>\log(a\times b)=\log a+\log b</math>.
* [http://www.att.com/ AT&T Inc.]

* [http://www.verizon.com/ Verizon Communications]
[[Loudness]]: Weber's law does not quite hold for loudness. It is a good approximation for higher amplitudes, but not for lower amplitudes. This is usually referred to as "near miss" to Weber's law.{{Fact|date=June 2008}}
* [http://www.cincinnatibell.com/ Cincinnati Bell]

* [http://biz.yahoo.com/ap/060305/at_t_bellsouth.html?.v=16 Yahoo! Finance Article] on AT&T's purchase of BellSouth
== See also ==
* [http://www.boston.com/news/local/maine/articles/2008/03/30/fairpoint_verizon_deal_comes_to_a_close_on_monday/ Boston.com - FairPoint-Verizon deal comes to a close on Monday]
* [[Stevens' power law]]
* [[Sone]]
* [[nervous system]]
* [[human nature]]

== References ==
{{nofootnotes|date=July 2008}}
{{refimprove|date=July 2008}}
*Jianhong (Jackie) Shen and Yoon-Mo Jung (2006), Appl. Math. Optim., 53(3):331-358, [http://www.springerlink.com/content/172467181w543245/?p=cab484b467b64e729a4666703e273f95&pi=3 ''Weberized Mumford-Shah model with Bose-Einstein photon noise''](Integrating Weber's Law <em>quantitatively</em> into modern computational vision and image processing).
*Jianhong (Jackie) Shen (2003), Physica D: Nonlinear Phenomena, 175(3/4):241-251, [http://dx.doi.org/10.1016/S0167-2789(02)00734-0 ''On the foundations of vision modeling I. Weber's law and Weberized TV (total variation) restoration''.]


<!--Categories-->
[[Category:Perception]]
[[Category:Behavioral concepts]]
[[Category:Bell System]]
[[Category:Psychophysics]]
[[Category:Telecommunications history]]


[[ja:地域ベル電話会社]]
[[bg:Закон на Вебер-Фехнер]]
[[fi:Yhdysvaltain alueelliset puhelinyhtiöt]]
[[de:Weber-Fechner-Gesetz]]
[[es:Ley de Weber-Fechner]]
[[fr:Loi de Weber-Fechner]]
[[he:חוק ובר-פכנר]]
[[it:Legge di Weber-Fechner]]
[[hu:Weber-törvény]]
[[nl:Wet van Weber]]
[[ja:ヴェーバー‐フェヒナーの法則]]
[[pl:Prawo Webera-Fechnera]]
[[ru:Закон Вебера — Фехнера]]
[[simple:Weber-Fechner law]]
[[sk:Weberov-Fechnerov zákon]]

Revision as of 22:30, 10 October 2008

"Baby Bell" redirects here. For Babybel cheese, see Babybel.
File:RBOC map.png
Map of the original and current companies.

The Regional Bell Operating Companies (RBOC) are the result of the U.S. Department of Justice antitrust suit against the former American Telephone & Telegraph Company (later known as AT&T Corp.)

History

On January 8, 1982, AT&T Corp. settled the suit and agreed to divest ("spin off") its local exchange service operating companies. Effective January 1, 1984, AT&T Corp.'s local operations were split into seven independent Regional Bell Operating Companies known as "Baby Bells." RBOCs were originally known as Regional Holding Companies, or RHCs [1].

After the Modification of Final Judgment, the resulting Baby Bells were originally:

Prior to 1984, AT&T Corp. also held investments in two smaller and otherwise independent companies, Cincinnati Bell and Southern New England Telephone (SNET). Following the 1984 breakup, these became fully independent as well. All nine local-exchange companies were assigned a share of the rights to the Bell trademark. Additionally, there was one comparably-sized independent (non-Bell) company, GTE.

Shared trademarks

After divestiture AT&T Corp. was prohibited from using the Bell name or logo (with the notable exception of AT&T's Bell Laboratories), and those trademarks would be shared by the RBOCs. Since the BellSouth acquisition, Cincinnati Bell has been the only former AT&T company still carrying the "Bell" name. (Additionally, Bell Canada, which was separated from AT&T in 1956, continues to use the "Bell" trademark, which it owns outright in Canada.)

Verizon continues to use the Bell logo on its payphones (including former GTE payphones), hard hats, trucks, and buildings. As well, Malheur Bell, an autonomous local phone company owned by Qwest, uses the Bell name and logo. In both cases, these are likely intended to display continued use in order to maintain the companies' respective trademark rights.

On the other hand, excluding historical documents and residual usage on the former BellSouth website, AT&T Inc. does not presently make any active use of the Bell marks.

Original 1984 Regional Holding Company logos

Mergers

Many of these companies have since merged, leaving only 3 regional telephone companies in the United States. After the 1984 breakup, part of AT&T Corp.'s Bell Labs was split off into Bellcore, which would serve as an R&D and standards body for the seven Baby Bells. In 1997, Bellcore was acquired by Science Applications International Corporation where it became a wholly owned subsidiary and was renamed Telcordia.[1]

AT&T Inc.

Southwestern Bell Corporation, which changed its name to SBC Communications in 1995, acquired Pacific Telesis in 1997, former independent Bell System franchise not part of divestiture, SNET in 1998, and Ameritech in 1999. In February 2005, SBC announced its plans to acquire former parent company AT&T Corp. for over $16 billion. SBC took on the AT&T name upon merger closure on November 18, 2005. SBC began trading as AT&T Inc. on December 1, 2005 but began re-branding as early as November 21. On March 5, 2006, it was announced that AT&T Inc. would purchase BellSouth for $67 billion U.S., in an all-stock deal. On December 29, 2006, the FCC approved the merger, worth $86 billion US. [1]

Verizon Communications

In 1997, NYNEX was acquired by Bell Atlantic (taking the Bell Atlantic name), which later, in 2000, merged with GTE, the largest independent telephone company, to form Verizon. In 2005, following a protracted bidding war with rival RBOC Qwest, Verizon announced that it would acquire long distance company MCI. The Verizon and MCI merger closed on January 6, 2006.

On January 16, 2007, Verizon announced that it would split off Verizon New England operations in Maine, New Hampshire, and Vermont into a separate operating company, which then will be spun off and merged with FairPoint Communications. The deal was completed on March 31, 2008.

Qwest

In 2000, US West was merged into Qwest, a Denver-based fiber optics long-distance company. Also provides internet, wireless, and local telephone services.[2]

Cincinnati Bell

  • The former independent Bell System franchise Cincinnati Bell, which was not part of the 1984 divestiture because AT&T only held a minority stake in the company, remains independent of the RBOCs.

Bell Canada

  • Bell Canada was divested from AT&T Corp. in 1956 and not part of the 1984 agreement.

Notes

  1. The acronym RHC for Regional Holding Company is also sometimes seen.

See also

References

  1. ^ Dr. J. Robert Beyster with Peter Economy, The SAIC Solution: How We Built an $8 Billion Employee-Owned Technology Company, John Wiley & Sons (2007) p.73
  2. ^ "Qwest Homepage". Qwest Communications International Inc. Retrieved 2008-01-20.

External links

Retrieved from "https://en.wikipedia.org/w/index.php?title=Weber–Fechner_law&oldid=244460667"